Details

sample1.6s

Algorithm: halfpoints

simplify5.8s

Counts

1 → 1

Iterations

Iter	Nodes
4	15340
3	1591
2	264
1	60
0	19

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize297.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.p16 i (+.p16 (+.p16 alpha beta) i))
0.2b	(*.p16 i (+.p16 (+.p16 alpha beta) i))
1.5b	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
3.4b	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

58×	`p16-times-frac`
38×	`/p16-rgt-identity-expand`
30×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
29×	`associate-/r/`
24×	`difference-of-squares`
13×	`associate-*r/`
11×	`associate-*l/`
8×	`associate-/r` `difference-of-sqr-1` `associate-/l`
6×	`associate-r`
5×	`associate-/l/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`p16-flip--`

Counts

4 → 122

Calls

4 calls:

14.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))
9.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))
8.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
8.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))
0.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))
0.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
0.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

simplify2.9s

Counts

126 → 126

Iterations

Iter	Nodes
3	6815
2	739
1	145
0	56

prune6.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.9b

localize326.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.8b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.5b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

478×	`p16-times-frac`
339×	`p16-lft-identity-expand` `p16--un-lft-identity`
323×	`*p16-rgt-identity-expand`
84×	`distribute-lft-out--`
48×	`p16-distribute-lft-out` `distribute-lft-out`
44×	`/p16-rgt-identity-expand`
42×	`distribute-rgt-out--`
38×	`associate-/r/`
37×	`associate-/r*`
24×	`distribute-rgt-out` `associate-/l*`
8×	`distribute-lft1-in`
5×	`associate-/l/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
1×	`associate-*r/` `p16-flip--`

Counts

4 → 404

Calls

4 calls:

135.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
91.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
19.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
15.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

simplify5.9s

Counts

408 → 408

Iterations

Iter	Nodes
3	7948
2	966
1	167
0	71

prune22.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.6b

localize498.0ms

Local error

Found 4 expressions with local error:

0.8b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
1.0b	(/.p16 i (+.p16 (+.p16 (+.p16 (real->posit16 1.0) alpha) (*.p16 (real->posit16 2) i)) beta))
1.2b	(/.p16 (+.p16 (+.p16 alpha i) beta) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

291×	`p16-times-frac`
210×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
84×	`distribute-lft-out--`
42×	`distribute-rgt-out--`
23×	`/p16-rgt-identity-expand`
21×	`associate-/r*`
19×	`associate-/l*`
18×	`associate-/r/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/l/`
1×	`p16-flip--`

Counts

4 → 254

Calls

4 calls:

74.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
74.0ms	(/.p16 i (+.p16 (+.p16 (+.p16 (real->posit16 1.0) alpha) (*.p16 (real->posit16 2) i)) beta))
40.0ms	(/.p16 (+.p16 (+.p16 alpha i) beta) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
14.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 i (+.p16 (+.p16 (+.p16 (real->posit16 1.0) alpha) (*.p16 (real->posit16 2) i)) beta))
0.0ms	(/.p16 (+.p16 (+.p16 alpha i) beta) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify2.8s

Counts

258 → 258

Iterations

Iter	Nodes
3	4850
2	873
1	147
0	64

prune16.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 0.5b

localize852.0ms

Local error

Found 4 expressions with local error:

0.8b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (-.p16 (.p16 i (real->posit16 2)) (real->posit16 1.0)) (+.p16 alpha beta)))
1.0b	(/.p16 i (+.p16 (+.p16 (+.p16 (real->posit16 1.0) alpha) (*.p16 (real->posit16 2) i)) beta))
1.2b	(/.p16 (+.p16 (+.p16 alpha i) beta) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

291×	`p16-times-frac`
238×	`p16-lft-identity-expand` `p16--un-lft-identity`
154×	`*p16-rgt-identity-expand`
56×	`p16-distribute-lft-out` `distribute-lft-out`
23×	`/p16-rgt-identity-expand`
21×	`associate-/r*`
19×	`associate-/l*`
17×	`associate-/r/`
14×	`distribute-rgt-out`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/l/`

Counts

4 → 253

Calls

4 calls:

58.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (-.p16 (.p16 i (real->posit16 2)) (real->posit16 1.0)) (+.p16 alpha beta)))
75.0ms	(/.p16 i (+.p16 (+.p16 (+.p16 (real->posit16 1.0) alpha) (*.p16 (real->posit16 2) i)) beta))
43.0ms	(/.p16 (+.p16 (+.p16 alpha i) beta) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
26.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (-.p16 (.p16 i (real->posit16 2)) (real->posit16 1.0)) (+.p16 alpha beta)))
0.0ms	(/.p16 i (+.p16 (+.p16 (+.p16 (real->posit16 1.0) alpha) (*.p16 (real->posit16 2) i)) beta))
0.0ms	(/.p16 (+.p16 (+.p16 alpha i) beta) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify1.5s

Counts

257 → 257

Iterations

Iter	Nodes
3	2784
2	603
1	134
0	62

prune15.2s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 0.5b

regimes2.0s

Accuracy

0% (0.9b remaining)

Error of 1.4b against oracle of 0.5b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
1	30
0	30

end0.0ms

sample32.4s

Algorithm: halfpoints